• Title/Summary/Keyword: Asymptotic Theory

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Integrated Structural Dynamic Response Analysis considering the UNDEX Shock Wave and Gas Bubble Pulse (수중폭발 충격파와 가스구체 압력파를 함께 고려한 구조물의 동적응답해석)

  • Lee, Sang-Gab;Hwon, Jeong-Il;Chung, Jung-Hoon
    • Journal of the Society of Naval Architects of Korea
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    • v.44 no.2 s.152
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    • pp.148-153
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    • 2007
  • Two typical impact loadings, shock wave and gas bubble pulse, due to UNDEX(UNDerwater EXplosion), should be considered together for the closest response analysis of structure subjected to UNDEX to a reality. Since these two impact loadings have different response time bands, however, their response characteristics of structure are different from each other. It is impossible to consider these effectively under the current computational environment and the mathematical model has not yet been developed. Whereas Hicks model approximates the fluid-structure interaction due to gas bubble pulse as virtual mass effect, treating the flow by the response of gas bubble after shock wave as incompressible ideal fluid contrary to the compressible flow due to shock wave, Geers-Hunter model could make the closest response analysis of structure under UNDEX to a real one as a mathematical model considering the fluid-structure interaction due to shock wave and gas bubble pulse together using acoustic wave theory and DAA(Doubly Asymptotic Approximation). In this study, the application and effectiveness of integrated dynamic response analysis of submerged structure was examined with the analysis of the shock wave and gas bubble pulse together.

Vertical Sectorization Techniques in MISO Downlink Active Antenna Systems (MISO 하향 능동 안테나 시스템에서의 수직 섹터분할 기법)

  • Ahn, Minki;Eom, Subin;Lee, Inkyu
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.40 no.6
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    • pp.997-1004
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    • 2015
  • In this paper, we study vertical sectorization techniques in multiple-input single-output (MISO) downlink active antenna systems (AAS). In the AAS, antenna beam patterns can be adjusted in each sector and multiple vertical beams can form the vertical sectorization. Since an exhaustive search based vertical sectorization algorithm requires high computational complexity to find the optimal tilt angles, we propose two vertical sectorization algorithms to reduce the complexity. First, we provide an asymptotic sum rate based algorithm which utilizes a large system approximation of the average sum rate based on the random matrix theory. Next, by using the result in the single sector transmission, the single sector based algorithm is proposed. In the simulation results, we confirm that the proposed algorithms are close to the performance of the exhaustive search algorithm with much reduced complexity.

Wave Responses and Ship Motions in a Harbor Excited by Long Waves(I) (항만내 파도응답과 계류선박의 운동해석(I))

  • I.H. Cho;Hang-S. Choi
    • Journal of the Society of Naval Architects of Korea
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    • v.29 no.2
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    • pp.38-47
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    • 1992
  • The motion response of a ship moored in a rectangular harbor excited by long waves has been studied theoretically and experimentally. Within the framework of potential theory, matched asymptotic expansion techniques are exployed to analyze the problem. The fluid domain is divided into the ocean and the harbor regions for the analysis of wave response in a harbor without ship. The wave responses in both the ocean and the harbor sides are solved first independently in terms of Green's functions, which are the solutions of the Helmholtz equation satisfying appropriate boundary conditions. Slender body approximations are used to obtain the velocity jumps across the ship, which are associated with the symmetric motion modes of the ship. Unknowns contained in each solution are finally determined by matching at an intermediate zone between two neighboring regions. Theoretical results predict the ship motion qualitatively well. The main source of quantitative discrepancies is presumably due to real fluid effects such as separation at the harbor entrance and friction on harbor boundaries.

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On the Improvement of the Accuracy of Higher Order Derivatives in the MLS(Moving Least Square) Difference Method via Mixed Formulation (MLS 차분법의 결정 변수에 따른 정확도 분석 및 혼합변분이론을 통한 미분근사 성능향상)

  • Kim, Hyun-Young;Kim, Jun-Sik
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.33 no.5
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    • pp.279-286
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    • 2020
  • In this study, we investigate the accuracy of higher order derivatives in the moving least square (MLS) difference method. An interpolation function is constructed by employing a Taylor series expansion via MLS approximation. The function is then applied to the mixed variational theorem in which the displacement and stress resultants are treated as independent variables. The higher order derivatives are evaluated by solving simply supported beams and cantilevers. The results are compared with the analytical solutions in terms of the order of polynomials, support size of the weighting function, and number of nodes. The accuracy of the higher order derivatives improves with the employment of the mean value theorem, especially for very high-order derivatives (e.g., above fourth-order derivatives), which are important in a classical asymptotic analysis.

Rheological Properties of the Solutions of Incompatible Polymer Blends

  • Sohn, Jeong-In;Ree, Taik-Yue
    • Bulletin of the Korean Chemical Society
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    • v.2 no.4
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    • pp.142-147
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    • 1981
  • A blend polymeric system composed of poly(methyl methacrylate) (PMMA or PM) and polystyrene (PS) dissolved in chloroform was rheologically studied. The viscosities ${\eta}_{bl}$ of the blend system with various blending ratios ${\chi}$ changing from zero (pure PS solution) to unity (pure PMMA solution) were measured at $25{\circ}C$ as a function of shear rates ${\dot{s}}$ by using a Couette type viscometer. ${\eta}_{bl}$ at a given ${\dot{s}}$ decreased exponentially with ${\chi}$ reaching asymptotic constant value of ${\eta}_{bl}$ ; ${\eta}_{bl}$ at a given ${\chi}$ is greater at a smaller ${\dot{s}}$. These results are explained by using Ree-Erying's theory of viscosity, ${\eta}_{bl}=(x_1{\beta}_1/{\alpha}_1)_{b}_1+ (x_2{\beta}_2/{\alpha}_2)_{bl}[sinh^{-1}{\beta}_2(bl) {\dot{s}}]/{\beta}_2(bl){\dot{s}}$. The Gibbs activation energy ${\Delta}G_i^\neq$(i = 2 for non-Newtonian units) entering into the intrinsic relaxation time ${\beta}$ is represented by a linear combination ${\Delta}G_i^\neq(bl) ={\chi}{\Delta}G_i^{\neq}_{iPM}+(1-{\chi}){\Delta}G_i^{\neq}_{iPS}$;the intrinsic shear modulus$[[\alpha}_i]^{-1}$ is also represented by $[{\alpha}_i(bl)]^{-1}={\chi}[{\alpha}_{iPM}]^{-1}+(1-{\chi})[{\alpha}_{iPS}]^{-1}$ and the fraction of area on a shear surface occupied by the ith flow units $x_i(bl)$ is similarly represented, i.e., $x_i(bl) = {\chi}x_{iPM}+(1-{\chi})x_{iPS}$. By using these ideas the Ree-Eyring equation was rewritten which explained the experimental results satisfactorily.

Permanent Magnet Synchronous Motor Control Algorithm Based on Stability Margin and Lyapunov Stability Analysis

  • Jie, Hongyu;Xu, Hongbing;Zheng, Yanbing;Xin, Xiaoshuai;Zheng, Gang
    • Journal of Power Electronics
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    • v.19 no.6
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    • pp.1505-1514
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    • 2019
  • The permanent magnet synchronous motor (PMSM) is widely used in various fields and the proportional-integral (PI) controller is popular in PMSM control systems. However, the motor parameters are usually unknown, which can lead to a complicated PI controller design and poor performance. In order to design a PI controller with good performance when the motor parameters are unknown, a control algorithm based on stability margin is proposed in this paper. First of all, based on the mathematical model of the PMSM and the least squares (LS) method, motor parameters are estimated offline. Then based on the estimation values of the motor parameters, natural angular frequency and phase margin, a PI controller is designed. Performance indices including the natural angular frequency and the phase margin are used directly to design the PI controller in this paper. Scalar functions of the d-loop and the q-loop are selected. It can be seen that the designed controller parameters satisfy Lyapunov large scale asymptotic stability theory if the natural angular frequencies of the d-loop and the q-loop are large than 0. Experimental results show that the parameter estimation method has good accuracy and the designed PI controller proposed in this paper has good static and dynamic performances.

Extremal Dependence in Asia Pacific Exchange Markets (EVT-Copula 모형을 이용한 아시아 외환시장 간 극단적 의존성에 관한 연구)

  • Kim, Tae-Hyuk;Zhao, Hui-Jing
    • The Korean Journal of Financial Management
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    • v.23 no.1
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    • pp.193-225
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    • 2006
  • The purpose of this paper is to analyze contagion in Asian foreign exchange markets using Extreme Value Theory and Copula. Our application deals with asymptotic dependence of daily exchange rate return for a sample of eight countries over period 1997.1.1-2005.4.13. The empirical results are summarized as follows. Firstly, Gumbel Copula is a good model to our data according to the value of AIC. Secondly, the extremal dependence between East Asian crisis countries became lower in the post crisis period than the crisis period. Thirdly, It seemed that high extremal dependence exists between East Asian countries with Singapore. Fourthly, the tail dependence between Indonesia, Malaysia, Thailand, Philippine became higher in the crisis period than the total period and post crisis period. Fifthly, the fact that the extremal dependence between Korea and Indonesia, Malaysia, Thailand, Philippine did not increase during the Asian Financial Crisis showed that the contagion effect was not the reason of the Korea's Fiancial Crisis. Sixthly, the extremal dependence between Asian exchange markets was not very high while comparing with the European exchange markets.

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A Bayesian Extreme Value Analysis of KOSPI Data (코스피 지수 자료의 베이지안 극단값 분석)

  • Yun, Seok-Hoon
    • The Korean Journal of Applied Statistics
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    • v.24 no.5
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    • pp.833-845
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    • 2011
  • This paper conducts a statistical analysis of extreme values for both daily log-returns and daily negative log-returns, which are computed using a collection of KOSPI data from January 3, 1998 to August 31, 2011. The Poisson-GPD model is used as a statistical analysis model for extreme values and the maximum likelihood method is applied for the estimation of parameters and extreme quantiles. To the Poisson-GPD model is also added the Bayesian method that assumes the usual noninformative prior distribution for the parameters, where the Markov chain Monte Carlo method is applied for the estimation of parameters and extreme quantiles. According to this analysis, both the maximum likelihood method and the Bayesian method form the same conclusion that the distribution of the log-returns has a shorter right tail than the normal distribution, but that the distribution of the negative log-returns has a heavier right tail than the normal distribution. An advantage of using the Bayesian method in extreme value analysis is that there is nothing to worry about the classical asymptotic properties of the maximum likelihood estimators even when the regularity conditions are not satisfied, and that in prediction it is effective to reflect the uncertainties from both the parameters and a future observation.

Adaptive Service Mode Conversion to Minimize Buffer Space Requirement in VOD Server (주문형 비디오 서버의 버퍼 최소화를 위한 가변적 서비스 모드 변환)

  • Won, Yu-Jip
    • Journal of KIISE:Computer Systems and Theory
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    • v.28 no.5
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    • pp.213-217
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    • 2001
  • Excessive memory buffer requirement in continuous media playback is a serious impediment of wide spread usage of on-line multimedia service. Skewed access frequency of available video files provides an opportunity of re-using the date blocks which has been loaded by one session for later usage. We present novel algorithm which minimizes the buffer requirement in multiple sessions of multimedia playbacks. In continuous media playback originated from the disk, a certain amount of memory buffer is required to synchronize asynchronous disk. Read operation and synchronous playback operation. As aggregate playback bandwodth increases, larger amount of buffer needs to be allocated for this synchronization purpose. The focus of this work is to study the asymptotic behavior of the synchronization buffer requirement and to develop an algorithm coping with this excessive buffer requirement under bandwidth congestioon. We argue that in a large scale continuous media server, it may not be necessary to read the blocks for each session directly from the disk. The beauty of our work lies in the fact that it dynamically adapts to disk utilization of the server and finds the optimal way of servicinh the individual sessions while minimizing the overall buffer space requirement. Optimality of the proposed algorithm is shown by proof. The effectiveness and performance of the proposed scheme is examined via simulation.

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